Improving American River Flood Frequency Analyses (1999) / Chapter Skim
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3 Flood Frequency Estimates for the American River
3 Flood Frequency Estimates for the American River
Pages 39-66
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From page 39... ...
Fitting a continuous mathematical distribution to data sets yields a compact and smoothed representation of the flood frequency distribution revealed by the available data, and a systematic procedure for extrapolation to flood discharges larger than those historically observed. While the American River flood record at Fair Oaks is almost 100 years in length, there is a goal of providing flood projection for at least the flood that has a chance of 1 in 200 of being exceeded in any year.
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From page 40... ...
of the weighted estimate is minimized by weighting the station and generalized skew coefficients inversely proportional to their individual mean square errors: 40 Improving American River Flood Frequency Analyses
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From page 41... ...
Alternative Treatments of Outliers and Historical and Paleoflood Information Both outliers and historical and paleoflood data can be handled in the framework of censored data. The influence of low outliers can be eliminated by censoring below a low threshold.
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From page 42... ...
, but it often has convergence problems for the logPearson type ITI. Alternative me~ods include distributional truncation (see Durrans, 1996~; partial probability weighted moments (Wang, 1990,1996; Kroll and Stedinger, 1996~; probability plot regression (Kroll and Stedinger, 1996~; EH-moments (Wang, 19971; and the Expected Moments Algorithm (Cohn et al., 1997~.
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From page 43... ...
An investigator must use professional judgment to a significant degree, though it is possible to obtain some guidance and insight through investigations of physical causes of flooding at a site, studies to assess the sensitivities of quartile estimates to the choice of censoring threshold, and comparisons with nearby hydrologically similar sites. Historical and Paleoflood Data As discussed in Chapter 2, historical and paleoflood information represents a censored sample because only the largest floods are recorded.
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From page 44... ...
This includes the assumption of the log-Pearson type III distribution and estimation based on preserving log-space moments. Estimation was based on traditional method of moments and the Expected Moments Algorithm.
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From page 45... ...
. · the skew map from Bulletin 17-B; · estimated log skews for maximum annual three-day rain flood discharges from the Feather River at Oreville, Yuba River at Marseille, Mokelumne River, Stanislaus River, Tuolumne River, and Merced River; and · two PMF estimates for the American River at Folsom Dam (three-day average flows of 401,000 cis and 485,000 cis)
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From page 46... ...
Efforts were employed to reject low outliers, but no effort was made to use historical information. 46 Improving American River Flood Frequency Analyses
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From page 47... ...
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From page 48... ...
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From page 49... ...
This regional skew estimate is based on log skews computed from maximum annual three-day rain flood data from seven large westsiope Sierra rivers ~JSACE, 1998~. For each of these discharge series there are about 25 more years of data than were used to construct the Bulletin 17-B skew map.
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From page 50... ...
The committee recommends that the regional skew value of -0.} be adopted as the weighted skew coefficient for the logarithms of the three-day rain flood discharges for the American River. The choice of the skew coefficient can be considered a critical decision and Bulletin 17-B encourages hydrologists to perform site-specific studies to improve estimates of the skewness coefficient.
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From page 51... ...
Alternative Frequency Estimates for the American River Data The committee chose five cases (with subcases) to explore alternate estimates ofthe probability distribution of three-day average rain flood discharges on the American River at Fair Oaks.
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From page 52... ...
Note that Cases 4a and 4b are intended to bracket the results of using the historical data with a skew estimated by EMA, while Case 4c gives a best estimate. Case 5: Systematic Record and Historical and Paleoflood Information with Skew Estimated byEMA (Sys.
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From page 54... ...
y cn 3 o a)
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From page 55... ...
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From page 56... ...
As suggested later in this report, it seems that the log-Pearson type III distribution has trouble describing the distribution from which the flood record is drawn without overestimating the magnitude of quartiles with return periods greater than 200 years. The committee does not try to quantify this mode!
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From page 57... ...
The difference is that Case 3c uses a refined and slightly different site-specific regional skewness coefficient with the available historical flood information for the American River. When the differences between the quartiles are viewed with the perspective provided by the 90 percent confidence intervals, they are quite close at the 200-year and even the 500-year return period event.
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From page 58... ...
were used; the censoring threshold was varied 5,000 cfs to 35,000 cfs, in increments of 5,000 cfs. (The median three-day flow is 22,340 cis; 35,000 cts has an estimated exceedance 58 Improving American River Flood Frequency Analyses
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From page 59... ...
To explore the extrapolation issue, the committee conducted some simple analyses using the precipitation data that it assembled for the American River basin. The object of these analyses was to gain insight into the possible shape of the upper tail of the American River flood frequency distribution, not to provide an alternative distribution estimate.
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From page 62... ...
It seems more likely that the distribution of three-day flood discharge bends downward for larger than observed discharges. Based on the precipitation data and a simple rainfall-runoff mode} it is possible to suggest how the discharge distribution might deviate from Me logPearson type III distribution for large discharges.
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From page 64... ...
Use of the paleoflood data implies that the log skew is much more negative, and as a result when the paleoflood data is used with the systematic and historical data, the resulting fitted log-Pearson type III distribution does not provide an adequate description of the flood flow frequency relationships for floods with exceedance probabilities from 0.5 up to and beyond 0.002. Frequency analysis based on a series of basin average precipitation data supports the latter possibility.
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From page 66... ...
If it is necessary to extrapolate the distribution for smaller exceedance probabilities, the recommended distribution provides a basis that is consistent with Bulletin 17-B guidelines, however, over estimation approaches should be investigated, including the rainfall-runoff approach explored by the committee. 66 Improving American River Flood Frequency Analyses
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